MetropolisHastingsMCMC

MetropolisHastingsMCMC.jl is a compact random-walk Metropolis–Hastings sampler. Its design mirrors BarkerMCMC.jl, retaining the LogDensityProblems.jl workflow while staying gradient-free thanks to plain Metropolis–Hastings proposals.

Installation

] add MetropolisHastingsMCMC

Usage

• Wrap an existing LogDensityProblems.jl model or pass a plain log-density function.
• Tune the number of iterations, initial step size σ, and target acceptance rate to suit your problem.

using MetropolisHastingsMCMC

log_p(x) = -0.5 * sum(x .^ 2)        # standard normal target

result = mh_mcmc(log_p, zeros(3); n_iter = 5_000)
result.samples
result.log_p

For a complete example with parameter transformations and automatic differentiation see the docs in docs/src/index.md.

References

• N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller (1953), Equation of State Calculations by Fast Computing Machines, Journal of Chemical Physics 21(6):1087–1092.
• W. K. Hastings (1970), Monte Carlo Sampling Methods Using Markov Chains and Their Applications, Biometrika 57(1):97–109.
• G. O. Roberts and J. S. Rosenthal (1997), An Overview of Recent Developments in Metropolis Algorithms, Journal of the Royal Statistical Society: Series B 59(4):781–804.

Lognormal Demo

The examples/lognormal_example.jl script showcases how to sample a univariate lognormal target distribution and visualise the resulting chain with CairoMakie.

julia --project=examples examples/lognormal_example.jl

Running the script saves a high-resolution PNG inside examples/. The figure pairs the trace with a smoothed density estimate and overlays the analytic lognormal density.